(a) To find \(P(X = 3)\), consider the outcomes where the maximum value is 3. The three-sided spinner can land on 3, and the five-sided spinner can land on 3, or the five-sided spinner can land on 3 while the three-sided spinner lands on 1 or 2. The possible outcomes are (3,3), (3,1), (3,2), (1,3), (2,3). Counting these outcomes gives 7 favorable outcomes out of 15 total possible outcomes, so \(P(X = 3) = \frac{7}{15}\).

(b) The probability distribution table for X is:

(c) To find \(E(X)\), use the formula \(E(X) = \sum x_i P(x_i)\):

\(E(X) = 1 \times \frac{2}{15} + 2 \times \frac{6}{15} + 3 \times \frac{7}{15} = \frac{2 + 12 + 21}{15} = \frac{35}{15} = \frac{7}{3}\).

To find \(Var(X)\), use the formula \(Var(X) = E(X^2) - (E(X))^2\):

\(E(X^2) = 1^2 \times \frac{2}{15} + 2^2 \times \frac{6}{15} + 3^2 \times \frac{7}{15} = \frac{2 + 24 + 63}{15} = \frac{89}{15}\).

\(Var(X) = \frac{89}{15} - \left(\frac{7}{3}\right)^2 = \frac{89}{15} - \frac{49}{9} = \frac{22}{45}\).